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Abstract
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In the game show "Let's Make a Deal," a contestant is shown three doors. The host Monty Hall tells the contestant that behind one of these doors is a brand new car. Behind each of the other doors is a goat. The contestant chooses a door, and then Monty (who knows what's behind each door) opens one of the remaining doors to reveal a goat. At this point, Monty gives the contestant a choice: "You can either open the door you chose initially, or you can switch to open the remaining door. You will win whatever is behind the door you open."
Does switching doors increase the contestant's chances of winning the car? Or does switching even matter? Using classic examples like the "Monty Hall problem," we will discuss some probability paradoxes, and how the underlying ideas relate to real-world statistical applications like hypothesis testing. |